ApoE4 dose effects on serum metabolome in Alzheimer’s Disease

a Data Science approach

George Miliarakis, MSc Thesis

15-01-2024

Data Exploration

The (interactive) correlation heatmap reveals very high correlation among aminoacids and TG compounds.

Differential expression of metabolites per ApoE genotype

Global test in AD group

Performing a Global Test on the serum metabolites of AD patients, correcting for sex (Ho: E4 status has no effect on metabolite levels, Ha: it has an effect), yields a significant difference (p = 0.029 ) between E4 carriers and non-carriers. The presence of ApoE4, correcting for sex seems to have an effect on the metabolites shown in the plot below. The most significantly affected metabolites are triglycerides, diglycerides (positively) and Îł-aminobutyric acid (negatively).

  p-value Statistic Expected Std.dev #Cov
1  0.0293      1.35    0.794   0.242  231

Performing a Global Test on ApoE4 dose shows distinct effects depeding on the number of ApoE4 alleles (p = 0.199).

  p-value Statistic Expected Std.dev #Cov
1  0.0199      1.22      0.8   0.169  231

Nested Linear Models

Metabolite-level models to test for ApoE4 dose effects. The F-tests yielded p-values < 0.05, however none of them survived FDR correction.

SCD and AD

The metabolites most affected by ApoE4 dose are D-L-3-aminoisobutyric.acid, histamine, L-serine, cerebroside D18.1.24.0, lysophosphatidyl-choline 18.1, phosphatidyl-choline 34.4, 36.6 and 40.4, sphingomyelin 22 and 24, LpH.PGE2, cLpH.PGA2, HpH.LPA.C20.5 and taurine.

Significant F-tests: 
                                p_values     p_adj
Am.DL.3.aminoisobutyric.acid 0.019274304 0.6617562
Am.Histamine                 0.010564489 0.6617562
Am.L.Serine                  0.029824862 0.6617562
Lip.Cer.d18.1.24.0.          0.021905538 0.6617562
Lip.LPC.O.18.1.              0.031940407 0.6617562
Lip.PC.34.4.                 0.034526409 0.6617562
Lip.PC.40.4.                 0.030049244 0.6617562
Lip.SM.d18.1.22.0.           0.028799960 0.6617562
Lip.SM.d18.1.24.0.           0.032508286 0.6617562
OS.LpH.PGE2                  0.033150673 0.6617562
OS.cLpH.PGA2                 0.031558866 0.6617562
OS.HpH.LPA.C20.5             0.009384457 0.6617562
Am.Taurine                   0.048562691 0.7013423
Lip.PC.O.36.6.               0.045023526 0.7013423

Dose effects on metabolites:
.id (Intercept) x1 ApoE4 x2 ApoE4
Am.DL.3.aminoisobutyric.acid -1.5490954 0.3318987 0.8154008
Am.DL.3.aminoisobutyric.acid 0.4134351 0.0859055 0.0081663
Am.Histamine 0.3195441 -0.5659714 -0.0265480
Am.Histamine 0.8658295 0.0037529 0.9304131
Am.L.Serine 0.0333628 0.3379990 -0.3722348
Am.L.Serine 0.9851888 0.0658654 0.1990250
Lip.Cer.d18.1.24.0. -0.0417257 0.4270800 0.6754568
Lip.Cer.d18.1.24.0. 0.9820991 0.0251655 0.0252529
Lip.LPC.O.18.1. 1.8656291 0.4080309 -0.2033259
Lip.LPC.O.18.1. 0.3018001 0.0273284 0.4834037
Lip.PC.34.4. 1.9741272 0.2164485 0.7565347
Lip.PC.34.4. 0.2780447 0.2418460 0.0105002
Lip.PC.40.4. 2.3598353 0.0213711 0.7079498
Lip.PC.40.4. 0.1671211 0.9016148 0.0106181
Lip.SM.d18.1.22.0. 0.7614513 0.4969492 0.4761153
Lip.SM.d18.1.22.0. 0.6893587 0.0111837 0.1216138
Lip.SM.d18.1.24.0. 1.4230810 0.5056344 0.3794747
Lip.SM.d18.1.24.0. 0.4567577 0.0100985 0.2178905
OS.LpH.PGE2 -3.3945165 0.4030782 -0.2497479
OS.LpH.PGE2 0.0697169 0.0344025 0.4040965
OS.cLpH.PGA2 -4.6375504 0.4328432 -0.2178364
OS.cLpH.PGA2 0.0164721 0.0272850 0.4789442
OS.HpH.LPA.C20.5 -0.6582008 -0.5979650 -0.2611871
OS.HpH.LPA.C20.5 0.7285528 0.0022985 0.3921756
Am.Taurine -0.6684682 0.3270235 -0.4141868
Am.Taurine 0.7360219 0.1061496 0.1951597
Lip.PC.O.36.6. -1.8817905 -0.4751836 -0.4010070
Lip.PC.O.36.6. 0.3262360 0.0156350 0.1937509

AD group only

Among AD patients, ApoE4 dose seems to have an effect on several triglycerides, diglycerides, L-glutamic acid, L-lysine, 2- and 3-hydroxybutyric acid, glutamic acid, 3-phosphoglyceric acid, phosphatidylcholin, sphyngomyelin, HpH.PAF.C17, phosphoethanolamine, imino-diacetate.

Significant F-tests: 
                                    p_values     p_adj
Lip.TG.52.3.                     0.002128748 0.2496400
Lip.TG.52.4.                     0.002585849 0.2496400
Lip.TG.54.5.                     0.004966959 0.2496400
Lip.TG.54.6.                     0.005426957 0.2496400
Lip.TG.56.6.                     0.003464999 0.2496400
Lip.TG.54.4.                     0.007750811 0.2845736
Lip.DG.36.3.                     0.008660937 0.2845736
Am.L.Glutamic.acid               0.011127623 0.3141256
Am.L.Lysine                      0.028681036 0.3141256
OA.OA01...2.hydroxybutyric.acid  0.020666789 0.3141256
OA.OA04...Glutamic.Acid          0.025302325 0.3141256
OA.OA18...3.Phosphoglyceric.acid 0.024813628 0.3141256
Lip.TG.50.2.                     0.027348399 0.3141256
Lip.TG.50.3.                     0.024166483 0.3141256
Lip.TG.52.2.                     0.023188871 0.3141256
Lip.TG.52.5.                     0.021890331 0.3141256
Lip.TG.56.7.                     0.017149208 0.3141256
Lip.TG.56.8.                     0.023831512 0.3141256
Lip.Cer.d18.1.24.0.              0.028242776 0.3141256
Lip.PC.O.34.3.                   0.020831975 0.3141256
OS.HpH.LPA.C18.3                 0.015373446 0.3141256
Lip.TG.51.3.                     0.031204970 0.3262338
Lip.TG.50.1.                     0.036088644 0.3451584
Lip.SM.d18.1.22.0.               0.036844964 0.3451584
OS.HpH.PAF.C16.0                 0.037517223 0.3451584
OA.OA17...3.Hydroxybutyric.acid  0.039302817 0.3476788
Lip.TG.54.3.                     0.041634484 0.3546641
Am.O.Phosphoethanolamine         0.043904743 0.3606461
OA.OA23...Iminodiacetate         0.047339603 0.3754520

Dose effects on metabolites:
.id (Intercept) x1 ApoE4 x2 ApoE4
Lip.TG.52.3. -1.4643782 1.2007214 1.1831106
Lip.TG.52.3. 0.6358058 0.0010862 0.0072690
Lip.TG.52.4. -0.1121429 1.0791483 1.0133654
Lip.TG.52.4. 0.9679217 0.0011411 0.0105351
Lip.TG.54.5. 1.2741030 1.0610276 0.8388477
Lip.TG.54.5. 0.6529190 0.0015469 0.0341720
Lip.TG.54.6. 0.2658980 0.9338129 0.9026945
Lip.TG.54.6. 0.9194230 0.0025351 0.0151562
Lip.TG.56.6. 2.5632970 1.2397864 1.0449996
Lip.TG.56.6. 0.4277371 0.0011921 0.0211104
Lip.TG.54.4. 0.2841003 1.1968788 0.7554508
Lip.TG.54.4. 0.9310659 0.0020188 0.0962076
Lip.DG.36.3. 0.0840839 1.1289266 1.0213961
Lip.DG.36.3. 0.9796341 0.0034506 0.0271826
Am.L.Glutamic.acid 1.1589949 1.1005617 0.6335507
Am.L.Glutamic.acid 0.7128623 0.0029035 0.1435525
Am.L.Lysine 0.5379920 -0.3539418 0.6661742
Am.L.Lysine 0.8465875 0.2524606 0.0836013
OA.OA01…2.hydroxybutyric.acid -4.5792935 0.5442059 0.6278205
OA.OA01…2.hydroxybutyric.acid 0.0223926 0.0143576 0.0210505
OA.OA04…Glutamic.Acid -3.5427289 0.8275798 0.9267894
OA.OA04…Glutamic.Acid 0.2404107 0.0159397 0.0271758
OA.OA18…3.Phosphoglyceric.acid -11.3526089 1.2305158 1.0944053
OA.OA18…3.Phosphoglyceric.acid 0.0086309 0.0096998 0.0559774
Lip.TG.50.2. 1.0021497 0.6057483 0.9960892
Lip.TG.50.2. 0.7178487 0.0534302 0.0113252
Lip.TG.50.3. 1.8117447 0.8093683 0.9455898
Lip.TG.50.3. 0.5411158 0.0170936 0.0230086
Lip.TG.52.2. -0.8964596 0.8696917 1.0859643
Lip.TG.52.2. 0.7835104 0.0199221 0.0182605
Lip.TG.52.5. 2.2526828 0.8276755 0.8847326
Lip.TG.52.5. 0.4348213 0.0124079 0.0281487
Lip.TG.56.7. -1.7517659 0.9374863 1.1233568
Lip.TG.56.7. 0.5962265 0.0135900 0.0159981
Lip.TG.56.8. -3.4819968 0.8381351 1.0251686
Lip.TG.56.8. 0.2689616 0.0192008 0.0198447
Lip.Cer.d18.1.24.0. -0.7877149 0.6230035 1.2301173
Lip.Cer.d18.1.24.0. 0.8124950 0.0950419 0.0092203
Lip.PC.O.34.3. 2.5817961 -0.9050800 -0.4233676
Lip.PC.O.34.3. 0.3625664 0.0058104 0.2721552
OS.HpH.LPA.C18.3 3.7385786 -0.8558650 -0.4609491
OS.HpH.LPA.C18.3 0.1485977 0.0041038 0.1879416
Lip.TG.51.3. -0.5053142 0.9783986 0.8657830
Lip.TG.51.3. 0.8813664 0.0121797 0.0655915
Lip.TG.50.1. 1.7033554 0.5403834 0.9621863
Lip.TG.50.1. 0.5363102 0.0807345 0.0134026
Lip.SM.d18.1.22.0. 2.2055258 0.7500179 1.0318359
Lip.SM.d18.1.22.0. 0.4908551 0.0385733 0.0216149
OS.HpH.PAF.C16.0 1.1277201 0.5195603 0.8984433
OS.HpH.PAF.C16.0 0.6645912 0.0759694 0.0145063
OA.OA17…3.Hydroxybutyric.acid -3.9513696 0.0280606 0.8053452
OA.OA17…3.Hydroxybutyric.acid 0.1137514 0.9174098 0.0199116
Lip.TG.54.3. 0.1130591 1.0658881 0.5687422
Lip.TG.54.3. 0.9755739 0.0122726 0.2602614
Am.O.Phosphoethanolamine 3.1131060 0.9995290 0.6354866
Am.O.Phosphoethanolamine 0.3773964 0.0133318 0.1869034
OA.OA23…Iminodiacetate -2.9181098 0.9915980 0.5951219
OA.OA23…Iminodiacetate 0.4091103 0.0142923 0.2171628

SCD group only

Among individuals with SCD, lipid metabolites were not affected as much as in the AD group, with only LPC and PC showing a difference. Aminoacids (glycine, taurine, L-serine, serotonine, L-glutamic acid, L-glutamic acid, phosphoethanolamine) and oxidative stress compounds were mostly affected in this group.

Significant F-tests: 
                            p_values     p_adj
Am.Glycine               0.003514740 0.3473546
Am.Taurine               0.002948325 0.3473546
OS.cLpH.PGA2             0.005011479 0.3473546
OS.HpH.LPA.C18.1         0.006040949 0.3473546
OS.cHpH.aLPA.C16.1       0.007960965 0.3662044
Am.Ethanolamine          0.013509392 0.4438800
OA.OA11...Succinic.acid  0.013146702 0.4438800
Am.L.Serine              0.017478101 0.4580221
Am.Serotonine            0.017922604 0.4580221
Am.O.Phosphoethanolamine 0.021914277 0.5040284
OS.cLpH.PGF2a            0.024487586 0.5120132
OS.LpH.PGE2              0.028774008 0.5515018
Am.L.Glutamic.acid       0.037526747 0.6165108
Lip.LPC.18.1.            0.035209617 0.6165108
OS.HpH.S.1.P.C18.1       0.040427658 0.6198908
Am.L.Aspartic.acid       0.049024437 0.6411695
Lip.PC.36.3.             0.045474810 0.6411695

Dose effects on metabolites:
.id (Intercept) x1 ApoE4 x2 ApoE4
Am.Glycine 0.3136001 0.8094015 -1.2299980
Am.Glycine 0.9288642 0.0049285 0.1199675
Am.Taurine -4.1889773 0.5828771 -2.0018238
Am.Taurine 0.2317949 0.0374504 0.0121757
OS.cLpH.PGA2 -4.9708116 0.6421668 -2.2210054
OS.cLpH.PGA2 0.2239471 0.0488834 0.0167946
OS.HpH.LPA.C18.1 -2.0076802 0.2572539 -2.1977631
OS.HpH.LPA.C18.1 0.5392303 0.3197481 0.0036995
OS.cHpH.aLPA.C16.1 -0.7226914 0.4097244 -1.6050636
OS.cHpH.aLPA.C16.1 0.8058507 0.0814836 0.0170329
Am.Ethanolamine -7.6872306 0.4741103 -1.2610213
Am.Ethanolamine 0.0107470 0.0434221 0.0565401
OA.OA11…Succinic.acid -2.6309618 0.7057740 -0.7535436
OA.OA11…Succinic.acid 0.4269017 0.0087414 0.3075400
Am.L.Serine -0.1446469 0.4478211 -1.5500162
Am.L.Serine 0.9648177 0.0876696 0.0375814
Am.Serotonine -5.4398488 0.6027268 -1.0048081
Am.Serotonine 0.0966104 0.0211071 0.1661665
Am.O.Phosphoethanolamine -7.2865376 0.5261461 -1.7376425
Am.O.Phosphoethanolamine 0.0639237 0.0888567 0.0476605
OS.cLpH.PGF2a -4.0168137 0.5612769 -1.6570842
OS.cLpH.PGF2a 0.3108338 0.0754429 0.0633847
OS.LpH.PGE2 -4.0593930 0.5430712 -1.7009626
OS.LpH.PGE2 0.3164788 0.0920321 0.0624149
Am.L.Glutamic.acid -2.7679866 0.1140449 -1.9281177
Am.L.Glutamic.acid 0.4226440 0.6744710 0.0144904
Lip.LPC.18.1. -4.5454870 0.5561727 -1.0740727
Lip.LPC.18.1. 0.1905223 0.0445592 0.1650333
OS.HpH.S.1.P.C18.1 -0.3190975 0.3557437 -1.5115974
OS.HpH.S.1.P.C18.1 0.9242884 0.1827166 0.0472202
Am.L.Aspartic.acid -0.0247712 -0.1948346 -1.9304107
Am.L.Aspartic.acid 0.9943290 0.4793053 0.0155843
Lip.PC.36.3. -1.2965704 0.5594230 -0.4703524
Lip.PC.36.3. 0.6698649 0.0227875 0.4877525

Multinomial Classification of ApoE4 presence and AD

The discriminative potential of the metabolites, correcting for clinical background features, on AD and ApoE4 or not (4-class response ADE4, AD, SCDE4, SCD)is assessed by first fitting a Multi-nomial Logistic Regression (benchmark model). The benchmark model fits only the clinical features. The model’s AUC is compared with the same model (with altered hyperparameters) fitting clinical variables + 230 metabolites. The metabolites are then projected to 6 latent ML-estimated factors and 3 more models are fitted: Multi-nomial Logistic Regression, Decision Tree and XGBoost fitting clinical variables + 6 factors. The models’ multi-class classification performance is compared using confusion matrices and AUCs.

Fitting a benchmark model: clinical characteristics only

Multi-class area under the curve: 0.8143

Confusion Matrix and Statistics

          Reference
Prediction   AD ADE4  SCD SCDE4
     AD    4756 2251    2   102
     ADE4  3736  904   31   119
     SCD     34  199 1892  4158
     SCDE4   74   46 2075  4321

Overall Statistics
                                          
               Accuracy : 0.4807          
                 95% CI : (0.4744, 0.4869)
    No Information Rate : 0.3522          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.2972          
                                          
 Mcnemar's Test P-Value : < 2.2e-16       

Statistics by Class:

                     Class: AD Class: ADE4 Class: SCD Class: SCDE4
Sensitivity             0.5530      0.2659     0.4730       0.4967
Specificity             0.8537      0.8176     0.7879       0.8628
Pos Pred Value          0.6688      0.1887     0.3011       0.6631
Neg Pred Value          0.7815      0.8746     0.8855       0.7592
Precision               0.6688      0.1887     0.3011       0.6631
Recall                  0.5530      0.2659     0.4730       0.4967
F1                      0.6054      0.2208     0.3680       0.5680
Prevalence              0.3482      0.1377     0.1619       0.3522
Detection Rate          0.1926      0.0366     0.0766       0.1749
Detection Prevalence    0.2879      0.1939     0.2544       0.2638
Balanced Accuracy       0.7034      0.5417     0.6304       0.6797

Regularized Multinomial Regression adding 230 metabolites

Multi-class area under the curve: 0.8338

Confusion Matrix and Statistics

          Reference
Prediction   AD ADE4  SCD SCDE4
     AD    5764 2368    0     5
     ADE4  2829  966    1    42
     SCD      4    6 1659  2836
     SCDE4    3   60 2340  5817

Overall Statistics
                                          
               Accuracy : 0.5751          
                 95% CI : (0.5689, 0.5813)
    No Information Rate : 0.3522          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.4076          
                                          
 Mcnemar's Test P-Value : < 2.2e-16       

Statistics by Class:

                     Class: AD Class: ADE4 Class: SCD Class: SCDE4
Sensitivity             0.6702     0.28412    0.41475       0.6686
Specificity             0.8526     0.86516    0.86251       0.8498
Pos Pred Value          0.7084     0.25169    0.36826       0.7077
Neg Pred Value          0.8288     0.88333    0.88408       0.8251
Precision               0.7084     0.25169    0.36826       0.7077
Recall                  0.6702     0.28412    0.41475       0.6686
F1                      0.6888     0.26692    0.39012       0.6876
Prevalence              0.3482     0.13765    0.16194       0.3522
Detection Rate          0.2334     0.03911    0.06717       0.2355
Detection Prevalence    0.3294     0.15538    0.18239       0.3328
Balanced Accuracy       0.7614     0.57464    0.63863       0.7592

Projection to Latent Factors

Multinomial Logistic Regression adding 6 factors

Multi-class area under the curve: 0.8178

Confusion Matrix and Statistics

          Reference
Prediction   AD ADE4  SCD SCDE4
     AD    5047 2100    4    91
     ADE4  3344  941   60   202
     SCD    115  215 1998  3271
     SCDE4   94  144 1938  5136

Overall Statistics
                                         
               Accuracy : 0.5313         
                 95% CI : (0.525, 0.5375)
    No Information Rate : 0.3522         
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.3593         
                                         
 Mcnemar's Test P-Value : < 2.2e-16      

Statistics by Class:

                     Class: AD Class: ADE4 Class: SCD Class: SCDE4
Sensitivity             0.5869      0.2768    0.49950       0.5903
Specificity             0.8637      0.8307    0.82604       0.8640
Pos Pred Value          0.6969      0.2069    0.35685       0.7024
Neg Pred Value          0.7965      0.8780    0.89519       0.7950
Precision               0.6969      0.2069    0.35685       0.7024
Recall                  0.5869      0.2768    0.49950       0.5903
F1                      0.6372      0.2368    0.41629       0.6415
Prevalence              0.3482      0.1377    0.16194       0.3522
Detection Rate          0.2043      0.0381    0.08089       0.2079
Detection Prevalence    0.2932      0.1841    0.22668       0.2960
Balanced Accuracy       0.7253      0.5537    0.66277       0.7272

Decision Tree

Multi-class area under the curve: 0.8176

Confusion Matrix and Statistics

          Reference
Prediction   AD ADE4  SCD SCDE4
     AD    5578 1904   56    95
     ADE4  2692 1241   58   155
     SCD    182  153 2704  5420
     SCDE4  148  102 1182  3030

Overall Statistics
                                         
               Accuracy : 0.5082         
                 95% CI : (0.502, 0.5145)
    No Information Rate : 0.3522         
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.3445         
                                         
 Mcnemar's Test P-Value : < 2.2e-16      

Statistics by Class:

                     Class: AD Class: ADE4 Class: SCD Class: SCDE4
Sensitivity             0.6486     0.36500     0.6760       0.3483
Specificity             0.8724     0.86362     0.7220       0.9105
Pos Pred Value          0.7308     0.29932     0.3197       0.6791
Neg Pred Value          0.8229     0.89496     0.9202       0.7198
Precision               0.7308     0.29932     0.3197       0.6791
Recall                  0.6486     0.36500     0.6760       0.3483
F1                      0.6872     0.32892     0.4341       0.4604
Prevalence              0.3482     0.13765     0.1619       0.3522
Detection Rate          0.2258     0.05024     0.1095       0.1227
Detection Prevalence    0.3090     0.16785     0.3425       0.1806
Balanced Accuracy       0.7605     0.61431     0.6990       0.6294

XGBoost Forest

Multi-class area under the curve: 0.8355

Confusion Matrix and Statistics

          Reference
Prediction   AD ADE4  SCD SCDE4
     AD    6432 2000   19     3
     ADE4  2079 1263   35   184
     SCD     24    6 1559  3086
     SCDE4   65  131 2387  5427

Overall Statistics
                                          
               Accuracy : 0.5944          
                 95% CI : (0.5882, 0.6005)
    No Information Rate : 0.3522          
    P-Value [Acc > NIR] : < 2.2e-16       
                                          
                  Kappa : 0.4336          
                                          
 Mcnemar's Test P-Value : < 2.2e-16       

Statistics by Class:

                     Class: AD Class: ADE4 Class: SCD Class: SCDE4
Sensitivity             0.7479     0.37147    0.38975       0.6238
Specificity             0.8744     0.89211    0.84947       0.8386
Pos Pred Value          0.7608     0.35468    0.33348       0.6775
Neg Pred Value          0.8666     0.89891    0.87810       0.8039
Precision               0.7608     0.35468    0.33348       0.6775
Recall                  0.7479     0.37147    0.38975       0.6238
F1                      0.7543     0.36288    0.35942       0.6496
Prevalence              0.3482     0.13765    0.16194       0.3522
Detection Rate          0.2604     0.05113    0.06312       0.2197
Detection Prevalence    0.3423     0.14417    0.18927       0.3243
Balanced Accuracy       0.8112     0.63179    0.61961       0.7312

Model Comparison

Observations:

  1. Adding serum metabolite information (either the full 230-metabolite matrix or its 6-factor projection) seems to increase the discriminatory power of the models.

  2. Fitting 6 ML-estimated factors obtained by the FMradio package (cummulatively explaining 30% of variace) yields increased classification performance, serving as a valuable dimension reduction technique for high-dimensional data.

  3. Looking at the confusion matrix and individual ROC curves, all models were able to discriminate better among certain classes (AD+E4/SCD+E4, AD+E4/SCD, AD-E4/SCD+E4 and AD-E4/SCD-E4) compared to others (AD+E4/AD-E4 and SCD+E4/SCD-E4).

AUC
Clinical features only 0.8143379
Clinical features + 230 metabolites 0.8338068
Clinical features + 6 latent factors 0.8177738
Decision Tree 0.8176124
XGBoost 0.8355013

Metabolite Covariance Network Analysis in AD

The covariance network analysis shows distinct metabolic “images” among ApoE4 carriers and non-carriers in AD. The network vertices and edges are distinct.

i = 1   | max diff = 1.1226918030e+00
i = 2   | max diff = 1.2908036134e-28
Converged in 2 iterations, max diff < 1.49e-08.
Step 1... determine cutoff point
Step 2... estimate parameters of null distribution and eta0
Step 3... compute p-values and estimate empirical PDF/CDF
Step 4... compute q-values and local fdr
Step 5... prepare for plotting


- Retained elements:  343 
- Corresponding to 1.3 % of possible edges 
 
Step 1... determine cutoff point
Step 2... estimate parameters of null distribution and eta0
Step 3... compute p-values and estimate empirical PDF/CDF
Step 4... compute q-values and local fdr
Step 5... prepare for plotting


- Retained elements:  376 
- Corresponding to 1.43 % of possible edges

GGMs showing distinct metabolic compositions among ApoE4 carriers (left), non-carriers(middle) and the differential edges (right).

Network statistics

Wilcoxon Signed Rank test between the network statistics of ApoE4 carriers and non-carriers. The test shows distinct centrality degrees and average number of negative and positive edges.

$PCE4YES.degree
[1] 0.001016491

$PCE4YES.nNeg
[1] 0.007252307

$PCE4YES.nPos
[1] 0.02813907

Distinct metabolite communities among ApoE4 carriers/non carriers